Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 680 · 40 sums

The method (Letters one side, numbers the other): Open brackets: a(x − b) = ax − ab. Fractions: multiply both sides by the LCM of the denominators — x/3 + x/4 = 14 → 4x + 3x = 168. Move letter terms to one side and numbers to the other (change the sign when a term crosses =), then divide. Word problems: consecutive numbers are n, n + 1, n + 2 …; ages in y years are age + y.

1. 1.A father is 30 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
2. 2.The length of a rectangle is 9 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
3. 3.Solve: m/3 + m/6 = 12. What is m?
4. 4.The length of a rectangle is 4 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
5. 5.Solve: 5(p − 3) = p + 21. What is p?
6. 6.A father is 34 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?
7. 7.A father is 16 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
8. 8.Solve: 7m + 11 = m + 23. What is m?
9. 9.Solve: 5y + 20 = y + 32. What is y?
10. 10.The length of a rectangle is 7 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
11. 11.Solve: 8x + 7 = 5x + 49. What is x?
12. 12.Solve: t/6 + t/2 = 12. What is t?
13. 13.Solve: 3n + 5 = n + 15. What is n?
14. 14.A father is 26 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
15. 15.Solve: 8n + 20 = 7n + 29. What is n?
16. 16.A father is 12 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
17. 17.Solve: n/4 + n/2 = 24. What is n?
18. 18.The sum of two consecutive whole numbers is 83. What is the smallest of them?
19. 19.A father is 14 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
20. 20.The length of a rectangle is 8 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
21. 21.The sum of two consecutive whole numbers is 29. What is the smallest of them?
22. 22.Solve: p/6 + p/3 = 15. What is p?
23. 23.Solve: 5(m − 1) = 3m + 23. What is m?
24. 24.The sum of three consecutive whole numbers is 114. What is the smallest of them?
25. 25.Solve: 8y + 18 = 5y + 51. What is y?
26. 26.The sum of two consecutive whole numbers is 61. What is the largest of them?
27. 27.Solve: 3x + 3 = x + 21. What is x?
28. 28.Solve: t/5 + t/2 = 14. What is t?
29. 29.The sum of two consecutive whole numbers is 95. What is the largest of them?
30. 30.The length of a rectangle is 13 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
31. 31.A father is 15 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
32. 32.Solve: 5(t − 3) = 3t + 1. What is t?
33. 33.The sum of two consecutive whole numbers is 29. What is the largest of them?
34. 34.The length of a rectangle is 3 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
35. 35.Solve: 5(x − 3) = 3x + 25. What is x?
36. 36.A father is 9 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
37. 37.The sum of three consecutive whole numbers is 36. What is the smallest of them?
38. 38.Solve: 7x + 14 = 6x + 19. What is x?
39. 39.Solve: 3(x − 1) = x + 1. What is x?
40. 40.Solve: t/2 + t/3 = 35. What is t?

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